OS 10.9 is beta software that is only available to registered developer only. Since you have it, you must be a developer so you need post your question on the developer forums as no support will be given for it on these forums, as by posting on these forums you are no doubt violating your NDA.
If you are not a developer then you obtained 10.9 from an illegitiamate source and are not entitled to any support.
I Have the same issue or very similar with an iPhone 4 GSM. I have tried all sorts of troubleshooting(edit Hosts file, uninstall iTunes, turn off or uninstall antivirus/firewall, run diagnostics, change USB port, run iTunes as Admin). Diagnostics run "OK". I have Win7 instead of Mac. The iphone was never jailbroken.
The iPhone was charging when got stuck in "apple and usb screen". Tried to restore a million times without success. Windows recognize iPhone and I put it on DFU. When restore is in process, it says "waiting for iPhone" and then the connection seems to get lost(maks the tipical sound) but iTunes tries again and then it passes this fase and the message changes to "Preparing iPhone for restore" and it gets stuck like this for ~8min, and it finally ends in error 4013. I looked through LOG files and the last steps are:
[03:11:04.0248] <Recovery Mode Device 0E703DE8>: Recovery mode succeeded
[03:11:04.0248] Finished Recovery Restore Phase: Successful
[03:26:05.0529] Recovery mode device disconnected
[03:26:05.0529] Device removed when in state Restoring, moving device to transition state
[03:26:05.0529] Changing state from 'Restoring' to 'Transitioning'
[03:26:05.0529] Creating timer to monitor transition
[03:26:15.0112] Restore completed, status:4013
[03:26:15.0112] Failure Description:
[03:26:15.0112] Depth:0 Error:Unexpected device state 'Recovery' expected 'RestoreOS'
Piece of knowledge: at first I was receiving error 1394 in an earlier stage - what happened was that I was using firmware 6.1.3. When I started using 7.0.3 I passed through that point.
Can anyone please help me?